Writings and reflections on the psychological effects of music have been written as far back, or further, than the year 500 BCE. In the time of Pythagoras, many believed that because our senses and perceptions of the world around us were so different, we could not count on them to explain the phenomenon of music. They trusted only in hard, scientific evidence based on mathematics and physics. 
In some ways these Greek scholars were correct. When gathering data on the human ear, the absolute threshold of hearing among people of the same age group is close, but every person is different. This gap in perception of sound becomes wider as we compare different age groups. Younger children tend to be able to hear much higher and lower frequencies than adults.  Therefore no two people hear sounds alike and their experiences when listening to music will be unique.
During the scientific revolution, scientists like Galileo helped to contribute important discoveries in the acoustical phenomenon of music. Some of these discoveries such as the harmonic series and consonance and dissonance were studied immensely. Galileo believed that consonance was the effect of a certain pattern of beating (or waves) on the ear drum while dissonance would create an irregular pattern. 
Some more modern writings discuss the idea of consonance and dissonance and its scientific explanations.  However, even these writings lead to an entirely different thought: the tonal system itself.  This system is different for different cultures (e.g. Western Music vs. Eastern Music). Who is to say that a consonance or dissonance has the same effect on someone here in the U.S. – where we are accustomed to Western scales and harmonies – as it would in the Middle East – whose people are comfortable with scales that include quarter tones and whose scales are different from those we have in Western music?
A couple hundred years after Pythagoras, Aristoxenus objected to the mathematical approach taken. He felt that it could not be explained fully without the senses. He stated that in order for music to have an effect, one must be able to recall the previous sonority from the one heard in real time. A melody cannot exist without having a successive nature. Experiencing one must be through both perception and memory. 
Some composers and artists of today do not write their music based on common practice theory. They write their music based on how the harmonic structure makes them feel. Composers, like Eric Whitacre, develop a style of music that surrounds the listener with what could be called an “ethereal environment”. The music provides the listener a feeling of being transported to another world. This cannot be explained by any scientific measurement but can only be understood through the senses of the listener. The composer associates a certain mood with a particular sonority and writes his/her harmonies based on the mood he/she wants to portray to their audience. Composers like Whitacre have taken the psychology of music beyond that of mathematical explanations and utilized the senses to create their masterpieces.
Understanding the way music affects our minds through the senses – and not just through the physics of sound waves – can allow us to see the methodology behind the composers who write with the intent to evoke more emotional response and create a connection with the listener on a whole new level.
 -Deutsch, Diana. 2001 “Psychology of music.” Grove Music Online. 27 Jan. 2019. http://0-www.oxfordmusiconline.com.lib.utep.edu/grovemusic/view/10.1093/gmo/9781561592630.001.0001/omo-9781561592630-e-0000042574.
 -Eric F. Clarke. 2001 “Musicology.” Grove Music Online. 27 Jan. 2019. http://0-www.oxfordmusiconline.com.lib.utep.edu/grovemusic/view/10.1093/gmo/9781561592630.001.0001/omo-9781561592630-e-0000046710.
 -Helmholtz, Hermann von. Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik (english translation). Braunschweig, 222. F. Vieweg, 1863.
 -Moore, Brian C.J. 2001 “Hearing and psychoacoustics.” Grove Music Online. 27 Jan. 2019. http://0-www.oxfordmusiconline.com.lib.utep.edu/grovemusic/view/10.1093/gmo/9781561592630.001.0001/omo-9781561592630-e-0000042531.